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Triangulated Equivalences Involving Gorenstein Projective Modules

Published online by Cambridge University Press:  20 November 2018

Yuefei Zheng  and
Zhaoyong Huang
Yuefei Zheng
Affiliation:
Department of Applied Mathematics, College of Science, Northwest A&F University, Yangling 712100, Shaanxi Province, China e-mail: [email protected]
Zhaoyong Huang
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, China e-mail: [email protected]
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Abstract

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For any ring $R$, we show that, in the bounded derived category ${{D}^{b}}(\text{Mod}\,R)$ of left $R$-modules, the subcategory of complexes with finite Gorenstein projective (resp. injective) dimension modulo the subcategory of complexes with finite projective (resp. injective) dimension is equivalent to the stable category $\underline{\text{GP}}(\text{Mod}\,R)\,(resp.\overline{GI}(Mod\,R))$ of Gorenstein projective (resp. injective) modules. As a consequence, we get that if $R$ is a left and right noetherian ring admitting a dualizing complex, then $\underline{\text{GP}}(\text{Mod}\,R)$ and $\overline{\text{GI}}(\text{Mod}\,R)$ are equivalent.

Keywords

18G2516E35triangulated equivalenceGorenstein projective modulestable categoryderived categoryhomotopy category
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 4 , 01 December 2017 , pp. 879 - 890
Copyright
Copyright © Canadian Mathematical Society 2017

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